Cubes and Cube Roots

Cube Roots

We understand that geometrically speaking, a cube is a three-dimensional object, like a square box, having six flat surfaces. The regular dice that you find in your favourite board game is an example of a cube. So let us now explore the mathematical concept of cube roots.

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What is a Cube Root?

Before we get into understanding what function a cube root performs, let us first understand what exactly a cube root is. Root as we now understand is the lowest number that can be multiplied by itself a certain number of times to get another number. Like in square root we multiply 5 by 5 to get 25 which means the square root of 5 is 25. Similarly, in cube root, we multiply the digit thrice to arrive at an answer we will elaborate it with an example shortly.

Purpose of Cube Roots

Next, we must understand what purpose does the solving of cube roots serve. Let me illustrate this with an example of everyday life. Suppose I am planning to shift my house from one town to another. Now I will need boxes to pack my stuff. I go to a shopkeeper and ask him for some boxes. The shopkeeper shows me some boxes and tells me that each of them is just 2 feet in its length, width and height. Now, I need to understand whether that size of the boxes will be sufficient to accommodate my belongings or not.

This is where cube roots come in very handy. Let me show you how:

First recall the formula of calculating volume.

Length × Width × Height

Apply this in our case, the boxes are 2 feet, all sides, therefore the calculation will be

2 × 2 × 2

The sum total of this will be 8. Since when we multiply 2 three times, we get 8. Now we know that every box has a space of 8 cubic feet. Once you have calculated this you know that this size of the box is good enough to carry your stuff. We also find out that the cube root of 8 is 2! Since we had to multiply 2, which is the lowest number here, thus, root, three times to get 8, therefore making 2 a cube root.

Point to Remember

  • Square root is when you multiply the lowest digit twice or two times to arrive at the number.
  • Cube root is when you multiply the lowest number thrice or three times to arrive at the number.

Symbol of a Cube Root

This is the symbol of the cube root. A radical sign with single digit ‘3’. You define other roots symbols also in similar fashion, only the number over the sign keeps changing. Where there are no numbers written, it is understood that it is a square root.

What are Perfect Cubes and Cube Roots?

Now that we know what a cube root is and where does it come handy, let us know what a perfect cube is. We define a perfect cube as an integer or a whole number as the cube root. In other words, where both the numbers, the cube root and the value are without any decimals or fractions. If we refer to the example above, both 2 (which is the cube root) and 8 (which is the value) are whole numbers, there are no decimals or fractions in the final result. Therefore, we can safely say that the 8 is a perfect cube.

Some Perfect Cubes

There are about 11 perfect cubes present in the mathematical tables. I am putting them down here for you to understand better what we mean when we say that a certain integer is a perfect cube.

Solved Example for You

Question 1: Find the cube root of 5832.

Answer : Resolving into prime factors

5832 = {2 × 2 × 2} {3 × 3 × 3} {3 × 3 ×3} = 2 × 2 × 3 = 18

Question 2: What are the cube roots?

Answer: It refers to a special value that we use in math. By using this value we can multiply the given number three times. For example, 5 × 5 × 5 = 125. Therefore, the cube root of 125 is 5. In the same way, the cube root of 216 is 6 (6 × 6 × 6 = 216).

Question 3: What is the formula of the cube root?

Answer: We use a cube root to give the cube root value of any number. Simply, the cube root formula is denoted by the power of 3 over the number such as n3, where the number represents the number whose cube roots need to be found. E.g. 103 = 1000 (10 × 10 × 10 = 1000).

Question 4: What is a perfect cube?

Answer: It refers to the result of multiplying a number three times by itself. In other words, we can say that they are the numbers that have the exact cube roots. For example, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, and so on.

Question 5: What does the total cube mean?

Answer: It means that the volume measures the amount of space an object takes up in height, width, and length.

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